In a semicircle, a square is drawn with its diagonal perpendicular to the diameter. It is 1 unit away from the center and 4 units away from the circumference. What is the area of the orange square?
The radius of the circle must = 5 since the diagonal is 1 unit from the center and 4 units from the circumference
Using the Pythagorean Theorem.....the length of the diagonal = sqrt ( 5^2 - 1)^2 = sqrt (24)
The side of the square = sqrt (24) /sqrt (2) = sqrt 12
The area of the square = (sqrt (12))^2 = 12